Question: Solve for $x$ and $y$ using elimination. ${-6x-2y = -30}$ ${-5x+2y = -14}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-11x = -44$ $\dfrac{-11x}{{-11}} = \dfrac{-44}{{-11}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-6x-2y = -30}\thinspace$ to find $y$ ${-6}{(4)}{ - 2y = -30}$ $-24-2y = -30$ $-24{+24} - 2y = -30{+24}$ $-2y = -6$ $\dfrac{-2y}{{-2}} = \dfrac{-6}{{-2}}$ ${y = 3}$ You can also plug ${x = 4}$ into $\thinspace {-5x+2y = -14}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ + 2y = -14}$ ${y = 3}$